Why doesn't water come out of tap/faucet at high pressure when I turn it on? (tap=faucet)
When I turn a tap on full and then put my thumb over the spout covering, say, 90% of it, then the water spurts out. If I turn it on to, say 10%, then the water dribbles out. 
What's the essential difference between the way that my thumb covers most of the hole and the way the tap valve opens that makes the water come out at a different pressure in either case?
 A: The reason is that there is a valve between you and a very high-pressure main pipe. The pressure is not equal across this opening--- it drops to nearly atomospheric pressure, and the water dribbles out at a rate determined by the size. The opening allows a fixed amount of water per unit time through, determined by the pressure drop and Bernoulli's law.
When you cover the opening with your thumb you initially make the water dribble out slower, and the pressure rises closer to that of the main, so it will rise closer to the pressure provided by the water utility. The spray rate is again determined by Bernoulli's law, but now for the much higher pressure in the tap. You can go up all the way to the pressure in the main as you cover more of the opening, and if you cover all the opening, you get the main pressure on your thumb.
A: It's the shape of the tap - in fact the very reason for their being a tap rather than just a valve on the end of the pipe.
When you open  the valve slightly the water does come out at high speed, hits the inside of the tap spout and is stopped - it then runs out of the tap at slow speed instead of spraying you.  
Imagine if you put your finger over the end of the tap to create a spray but then collected that spray in another pipe and looked at the water coming out of the other end of the pipe - it would be a slow trickle, just like the tap.
